cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-20 of 1788 results. Next

A004934 a(n) = floor(n*phi^19), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 9349, 18698, 28047, 37396, 46745, 56094, 65443, 74792, 84141, 93490, 102839, 112188, 121537, 130886, 140235, 149584, 158933, 168282, 177631, 186980, 196329, 205678, 215027, 224376, 233725
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004925.
Cf. A004926, A004927, A004928, A004929, A004930, A004931, A004932.
Cf. A004933, A004935, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((9349+4181*Sqrt(5))*n/2): n in [0..60]]; // G. C. Greubel, Sep 12 2023
  • Mathematica
    Floor[GoldenRatio^(19)*Range[0, 60]] (* G. C. Greubel, Sep 12 2023 *)
  • SageMath
    [floor(golden_ratio^(19)*n) for n in range(61)] # G. C. Greubel, Sep 12 2023

A004920 a(n) = floor(n*phi^5), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 133, 144, 155, 166, 177, 188, 199, 210, 221, 232, 243, 255, 266, 277, 288, 299, 310, 321, 332, 343, 354, 365, 377, 388, 399, 410, 421, 432, 443, 454, 465, 476, 487, 499, 510, 521, 532, 543, 554, 565, 576, 587, 598
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004921, A004922, A004923, A004924, A004925, A004926.
Cf. A004927, A004928, A004929, A004930, A004931, A004932, A004933.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((11+5*Sqrt(5))*n/2): n in [0..60]]; // G. C. Greubel, Aug 22 2023
  • Mathematica
    Table[Floor[n GoldenRatio^5],{n,0,54}] (* Stefano Spezia, Feb 19 2023 *)
  • SageMath
    [floor(golden_ratio^5*n) for n in range(61)] # G. C. Greubel, Aug 22 2023

A004921 a(n) = floor(n*phi^6), phi = golden ratio, A001622.

Original entry on oeis.org

0, 17, 35, 53, 71, 89, 107, 125, 143, 161, 179, 197, 215, 233, 251, 269, 287, 305, 322, 340, 358, 376, 394, 412, 430, 448, 466, 484, 502, 520, 538, 556, 574, 592, 610, 628, 645, 663, 681, 699, 717, 735, 753, 771
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004922, A004923, A004924, A004925, A004926.
Cf. A004927, A004928, A004929, A004930, A004931, A004932, A004933.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622, A098317.

Programs

  • Magma
    [Floor((9+4*Sqrt(5))*n): n in [0..50]]; // G. C. Greubel, Aug 22 2023
  • Mathematica
    Floor[GoldenRatio^6*Range[0, 50]] (* G. C. Greubel, Aug 22 2023 *)
  • SageMath
    [floor((9+4*sqrt(5))*n) for n in range(51)] # G. C. Greubel, Aug 22 2023

Formula

From G. C. Greubel, Aug 22 2023: (Start)
a(n) = floor((9 + 4*sqrt(5))*n).
a(n) = floor((A098317)^2*n). (End)

A004923 a(n) = floor(n*phi^8), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 46, 93, 140, 187, 234, 281, 328, 375, 422, 469, 516, 563, 610, 657, 704, 751, 798, 845, 892, 939, 986, 1033, 1080, 1127, 1174, 1221, 1268, 1315, 1362, 1409, 1456, 1503, 1550, 1597, 1644, 1691, 1738, 1785
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004924, A004925, A004926.
Cf. A004927, A004928, A004929, A004930, A004931, A004932, A004933.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((47+21*Sqrt(5))*n/2): n in [0..60]]; // G. C. Greubel, Aug 24 2023
  • Mathematica
    With[{c=GoldenRatio^8},Floor[c*Range[0,40]]] (* Harvey P. Dale, Sep 08 2020 *)
  • SageMath
    [floor(golden_ratio^8*n) for n in range(61)] # G. C. Greubel, Aug 24 2023

A004925 a(n) = floor(n*phi^10), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 122, 245, 368, 491, 614, 737, 860, 983, 1106, 1229, 1352, 1475, 1598, 1721, 1844, 1967, 2090, 2213, 2336, 2459, 2582, 2705, 2828, 2951, 3074, 3197, 3320, 3443, 3566, 3689, 3812, 3935, 4058, 4181
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004926.
Cf. A004927, A004928, A004929, A004930, A004931, A004932, A004933.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622 (phi).

Programs

  • Magma
    [Floor((123+55*Sqrt(5))*n/2): n in [0..60]]; // G. C. Greubel, Aug 27 2023
  • Maple
    A004925:=n->floor(n*((1 + sqrt(5))/2)^10): seq(A004925(n), n=0..100); # Wesley Ivan Hurt, Jul 26 2017
  • Mathematica
    Floor[GoldenRatio^(10)*Range[0,60]] (* G. C. Greubel, Aug 27 2023 *)
  • SageMath
    [floor(golden_ratio^(10)*n) for n in range(61)] # G. C. Greubel, Aug 27 2023

A004927 a(n) = floor(n*phi^12), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 321, 643, 965, 1287, 1609, 1931, 2253, 2575, 2897, 3219, 3541, 3863, 4185, 4507, 4829, 5151, 5473, 5795, 6117, 6439, 6761, 7083, 7405, 7727, 8049, 8371, 8693, 9015, 9337, 9659, 9981, 10303, 10625
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004925.
Cf. A004926, A004928, A004929, A004930, A004931, A004932, A004933.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((161+72*Sqrt(5))*n): n in [0..60]]; // G. C. Greubel, Aug 27 2023
  • Mathematica
    Floor[GoldenRatio^(12)*Range[0,60]] (* G. C. Greubel, Aug 27 2023 *)
  • SageMath
    [floor(golden_ratio^(12)*n) for n in range(61)] # G. C. Greubel, Aug 27 2023

A004929 a(n) = floor(n*phi^14), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 842, 1685, 2528, 3371, 4214, 5057, 5900, 6743, 7586, 8429, 9272, 10115, 10958, 11801, 12644, 13487, 14330, 15173, 16016, 16859, 17702, 18545, 19388, 20231, 21074, 21917, 22760, 23603, 24446
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004925.
Cf. A004926, A004927, A004928, A004930, A004931, A004932, A004933.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((843+377*Sqrt(5))*n/2): n in [0..60]]; // G. C. Greubel, Sep 05 2023
  • Mathematica
    Floor[GoldenRatio^(14)*Range[0, 60]] (* G. C. Greubel, Sep 05 2023 *)
  • SageMath
    [floor(golden_ratio^(14)*n) for n in range(61)] # G. C. Greubel, Sep 05 2023

A004931 a(n) = floor(n*phi^16), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 2206, 4413, 6620, 8827, 11034, 13241, 15448, 17655, 19862, 22069, 24276, 26483, 28690, 30897, 33104, 35311, 37518, 39725, 41932, 44139, 46346, 48553, 50760, 52967, 55174, 57381, 59588, 61795
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004925.
Cf. A004926, A004927, A004928, A004929, A004930, A004932, A004933.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((2207+987*Sqrt(5))*n/2): n in [0..60]]; // G. C. Greubel, Sep 06 2023
  • Mathematica
    Floor[GoldenRatio^(16)*Range[0, 60]] (* G. C. Greubel, Sep 06 2023 *)
  • SageMath
    [floor(golden_ratio^(16)*n) for n in range(61)] # G. C. Greubel, Sep 06 2023

A004933 a(n) = floor(n*phi^18), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 5777, 11555, 17333, 23111, 28889, 34667, 40445, 46223, 52001, 57779, 63557, 69335, 75113, 80891, 86669, 92447, 98225, 104003, 109781, 115559, 121337, 127115, 132893, 138671, 144449, 150227
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004925.
Cf. A004926, A004927, A004928, A004929, A004930, A004931, A004932.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((2889+1292*Sqrt(5))*n): n in [0..60]]; // G. C. Greubel, Sep 11 2023
  • Mathematica
    With[{p=GoldenRatio^18},Floor[p*Range[0,30]]] (* Harvey P. Dale, Mar 06 2022 *)
  • SageMath
    [floor(golden_ratio^(18)*n) for n in range(61)] # G. C. Greubel, Sep 11 2023

A004935 a(n) = floor(n*phi^20), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 15126, 30253, 45380, 60507, 75634, 90761, 105888, 121015, 136142, 151269, 166396, 181523, 196650, 211777, 226904, 242031, 257158, 272285, 287412, 302539, 317666, 332793, 347920, 363047, 378174
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

From Joerg Arndt, Sep 12 2023: (Start)
phi^20 = 15126.999933893... is a near integer.
Therefore the (incorrect!) g.f. 1 + (-1 + 15128*x)/(1-x)^2 produces the initial about 15000 terms of this sequence.
(End)

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004925.
Cf. A004926, A004927, A004928, A004929, A004930, A004931, A004932.
Cf. A004933, A004934, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((15127+6765*Sqrt(5))*n/2): n in [0..60]]; // G. C. Greubel, Sep 12 2023
  • Mathematica
    With[{c=GoldenRatio^20},Floor[c Range[0,30]]] (* Harvey P. Dale, Feb 18 2013 *)
  • SageMath
    [floor(golden_ratio^(20)*n) for n in range(61)] # G. C. Greubel, Sep 12 2023
Previous Showing 11-20 of 1788 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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